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Gina is asked to identify a rational expression. Which of the following could she choose? Choose one CORRECT answer

A). 5.3/2x-1
B). x^3/2 + 5/2x^9
C). 8x^2 + 7/0
D). 9x-4/8+√x

3 answers

A rational expression is defined as a fraction where both the numerator and the denominator are polynomials. Let's evaluate the options:

A) \( \frac{5.3}{2x - 1} \) - The numerator (5.3) is a constant (which is a polynomial of degree 0) and the denominator (2x - 1) is a polynomial of degree 1. This is a rational expression.

B) \( \frac{x^3}{2} + \frac{5}{2x^9} \) - The first part \( \frac{x^3}{2} \) is a polynomial term, but the second part \( \frac{5}{2x^9} \) does not form a single rational expression because of division by a variable raised to a power in the denominator.

C) \( \frac{8x^2 + 7}{0} \) - Division by zero is undefined, so this does not qualify as a rational expression.

D) \( \frac{9x - 4}{8 + \sqrt{x}} \) - The denominator \( 8 + \sqrt{x} \) is not a polynomial because \( \sqrt{x} \) is not a polynomial term.

The only correct answer among the options provided is:

A) \( \frac{5.3}{2x - 1} \).

Now, let's answer a different question:
Melany was asked to create an equivalent form of the rational expression −3x2−15x−18x+3 . Which of the following is a correct equivalent form?
−3x−24−114x+3
This rational expression does not have any equivalent forms.
−3x−114
−3x−6

To determine an equivalent form of the rational expression \(-\frac{3x^2 - 15x - 18}{x + 3}\), we should first simplify it.

  1. Factor the numerator: \(-3x^2 - 15x - 18\) can be factored out:

    \[ -3(x^2 + 5x + 6) = -3(x + 2)(x + 3) \]

So, the expression becomes:

\[ -\frac{3(x + 2)(x + 3)}{x + 3} \]

  1. Cancel the common factors: As long as \(x + 3 \neq 0\) (or \(x \neq -3\)), we can cancel \(x + 3\) from the numerator and the denominator:

\[ -3(x + 2) \]

  1. Final form: This simplifies to:

\[ -3x - 6 \]

Now we can check the provided options:

  1. −3x−24−114x+3
  2. This rational expression does not have any equivalent forms.
  3. −3x−114
  4. −3x−6

Among these options, the correct equivalent form of the original rational expression is:

−3x−6.